Identifying Binomial Distributions. In Exercises 5–12, determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial). For those that are not binomial, identify at least one requirement that is not satisfied.

Credit Card Survey In an AARP Bulletin survey, 1019 different adults were randomly selected without replacement. Respondents were asked if they have one or more credit cards, and responses were recorded as “yes” and “no.”

A sample of 1019 adults is surveyed and is made to answer the question “if they have one or more credit cards.” The response is either “yes” or “no.”

The following assumptions of the binomial distribution should be satisfied:

• The procedure should have a fixed number of trials.
• The trials should be independent.
• Each trial should have outcomes that are of exactly two kinds: success and failure.
• The probability of success should be the same for all the trials.

The number of trials is fixed and holds a value equal to 1019.

It is given that 1019 adults were selected for a survey without replacement.

Thus, they cannot be considered independent unless they fulfill the 5% rule of cumbersome calculations, which says that the sample size should be no more than 5% of the population size.

It is given that the population of adults is considered.

Therefore, it can be safely said that a sample of 1019 adults is no more than 5% of the population of all adults.

Since the sample size is less than 5% of the population size, the selections can be considered independent.

The outcomes of the event whose probability is to be estimated must be of exactly two types.

One of the outcomes is regarded as a success, while the other is considered a failure.

Here, the response to the question has exactly twopossible outcomes.

Since all the 1019 adults have answered the same question, the probability of success for all trials is the same.

Since all the assumptions are met, the given situation can be modeled using the binomial distribution.